Statistical Model for Surface Fracture

We analyse the fracture dynamics of a thin film which covers an elastic substrate subject to stretching. The system is modelled through its one-dimensional electrical analogue: a two-layer system (ladder network) with large conductors on one level and random fuses on the other. The fragmentation process exhibits two different regimes, depending on whether the mean fragment size is large or small compared to an intrinsic correlation length. In the latter case we find a power law dependence of the mean fragment size on the externally applied current, the exponent depending on the distribution of the fuse strengths.